I know that some of the guys here use sandpaper with good success. Personally, I prefer to use pumice stone and razor hones, as there is no chance of leaving sandpaper grit imbedded in the leather strop which plays the very devil with a razor edge. Just go from course to light grit on whatever you choose.

If you use sandpaper you run the risk of having some of the abrasive particles left behind embedded in the leather. Use pumice stone instead on the nicks to sand them down.

Try using a nylon scrub pad and some GOJO or GOOP to clean up the strop and smooth over the scuff marks. If that does not remove the scuff marks then use a pumice stone.
Follow the nap(grain) of the leather.

If the strop is dry apply some kind of leather conditioner on the back of the strop a couple of times and give it a couple of days in between applications to sink in. On the face side of the strop use the conditioner sparingly. One or to pea sized drops worked into the leather with the heel of your hand. What you are trying to avoid is a goopy, sticky surface.

Finish it off by taking a glass bottle and rubbing the face of the strop for an hour. Do this for a couple of days. Then it should be ready for use.

The above is a summary of the recommendations from the posts on the SRP Yahoo forum over the past couple of years plus my own experiences in restoring strops.